Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. The first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM).

Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.

这里介绍的是一种用于时域随机地震波传播分析的模块化方法。所提出的方法旨在分析作为输入的不确定地震运动，通过不确定材料传播。不确定波传播的传统方法依赖于包含深基岩、局部土壤位置及其随机过程和随机场信息的模型。这样的模型会变得非常大并且在计算上难以处理。本文提出的模块化方法具有两步法，允许单独考虑深基岩和局部地点以及相应的随机场信息。第一步考虑基岩中的辅助随机运动问题。然后可以在距表面一定深度内的缩小域中模拟随机局部站点响应。在深度应用不确定的地震运动，对于局部不确定的站点响应，使用通过域缩减方法开发的随机有效力来完成。通过使用 Hermite 多项式混沌展开来表示材料参数的非高斯随机场和地震运动的非平稳随机过程，所提出的模块化方法是使用侵入式随机伽辽金方法制定的，如随机弹塑性有限元方法中所见(SEPFEM)。

使用三种情况的一维随机地震波传播分析说明了开发的模块化方法，并且模拟结果也与传统方法的结果进行了验证。